# Phase 5: Demographic Bartik Instrument — Interpretation Notes

## Summary

The Bartik (shift-share) instrument uses the interaction of country-specific
initial age structures (1990 shares) with global demographic trends to
generate exogenous variation in demographics.

## Key Findings

### 1. First Stage is Extremely Strong
- Model A2_Bartik_2SLS: Z₁ first-stage F = 421.4

F-statistics far exceed Stock-Yogo critical values, ruling out weak instrument concerns.

### 2. Rotemberg Weights — Which Age Groups Drive Identification?
- Age 0-4: weight = 1.1453, Wald estimate = -21.433
- Age 45-49: weight = 0.0448, Wald estimate = 11.904
- Age 50-54: weight = 0.0234, Wald estimate = 5.776

**6 age groups have negative weights**, suggesting some heterogeneity in the first stage.

### 3. Leave-One-Out Sensitivity
**WARNING**: Sign changes across LOO specifications suggest fragile identification.

### 4. Exclusion Restriction Concerns

The key threat to Bartik identification: global aging trends might affect
country i's current account through channels OTHER than demographics:

1. **Global interest rates**: Global aging → lower global rates → affects all countries
   regardless of their own demographics. Mitigated by controlling for interest rates,
   but not fully.

2. **Trade composition**: Global aging changes demand patterns (more healthcare,
   less investment goods) → affects trade-dependent economies. Not captured by
   domestic demographics.

3. **Commodity prices**: Global aging → lower growth → lower commodity demand →
   affects commodity exporters. Partially controlled by NFA and trade openness.

**Assessment**: The exclusion restriction is stronger for small open economies
(where global trends are truly exogenous) but weaker for large economies
(US, China, Japan) that contribute substantially to global trends. This is
a fundamental limitation of the Bartik approach in this setting.

### 5. Subsample Stability
- Full: OLS Z₁ = 40.482 (p=0.004)**, N=3231
- Ex-CCA: OLS Z₁ = 33.225 (p=0.018)*, N=2947
- Developing only: OLS Z₁ = 23.790 (p=0.193), N=1702
- OECD-like: OLS Z₁ = 34.851 (p=0.083), N=1168
- Post-2000: OLS Z₁ = 20.183 (p=0.223), N=2568
- Pre-2010: OLS Z₁ = 38.073 (p=0.035)*, N=1914

## Implications for the Paper

1. **The Bartik instrument confirms the demographic-CA relationship in the
   reduced form** — global aging trends interacting with initial age structures
   predict current accounts.

2. **However, the 2SLS estimates are unstable** (as shown in Phase 2),
   suggesting the Bartik variation may capture GE effects rather than
   pure country-level demographic channels.

3. **Rotemberg weights identify which age groups drive the result** — useful
   for understanding mechanisms (working-age vs. elderly shares).

4. **The exclusion restriction is debatable** — Bartik provides suggestive
   but not definitive causal evidence for the demographic-CA channel.

5. **Report as supplementary evidence**, not the main identification strategy.
   The Bartik reduced form is more credible than the 2SLS.
